Abstract

A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.

Received 15 March 2011Revised 07 January 2012Accepted 10 January 2012Published online 15 March 2012

Acknowledgments:

The authors have discussed the substance of this paper with several of their colleagues. At the risk of omitting some relevant names, they would like to especially thank James G. McDaniel, William M. Carey, William L. Siegmann, and Richard B. Evans. A.G.T. would like to thank the General Electric Company for its support of his efforts associated with the work reported here.